Statistical comparison of the slopes of two regression lines: A tutorial

Area of Science:

• Analytical Chemistry
• Statistical Modeling

Background:

• Comparing regression line slopes is a frequent task in analytical laboratories.
• Current methods using Student's t-test lack consensus on employing standard errors of slopes versus standard errors of regressions.

Purpose of the Study:

• To review fundamental concepts of the Student's t-test for comparing regression slopes.
• To investigate differences arising from using standard errors of slopes versus standard errors of regressions via Monte Carlo simulations.

Main Methods:

• Review of statistical principles for Student's t-test in regression analysis.
• Monte Carlo simulations to compare two approaches for calculating pooled standard error.
• Analysis of covariance (ANCOVA) as an alternative method.

Main Results:

• For small sample sets, typical in analytical labs, the Student's t-test based on the standard error of regression models is recommended.
• Equality of model variances is a critical factor for accurate comparisons.

Conclusions:

• The standard error of regression models is the appropriate choice for Student's t-test when comparing slopes in small analytical datasets.
• Attention to variance equality and consideration of ANCOVA are important for robust statistical comparisons.